King of the hills … Franz Klammer on the slopes at Bad Kleinkirchheim. Photograph: Daniel Gollner

Because they live and hunt alone, there is no collective noun for cougars. Though I wouldn't apply this piece of zoological trivia to the huddle of excited skiers, among them a significant number of expensively maintained femmes d'un certain âge, waiting to meet their hero at the Kaiserburgbahn lift station in Bad Kleinkirchheim, Austria, early one winter morning.

At 60, Franz Klammer remains a charismatic and ruggedly dishy figure, along Liam Neeson lines. Add to that his status as the greatest downhill skier in history, and the annual ski day he hosts in his boyhood resort for a group of lucky punters chosen in a lottery, and it sends a frisson of macho glamour into the crisp Carinthian air. His still-unsurpassed achievements in Austria's national sport – 26 World Cup wins plus a legendary hell-for-leather Olympic victory in Innsbruck in 1976 –make him something akin to Pelé in his country, but he arrives with no surly manager, no controlling PR and no security. This makes for some initial awkwardness, as we all pretend not to be desperate to share his chairlift, apart from a Viennese Mrs Robinson in snug tangerine ski pants who swiftly sidles into the Klammer-flanking position she will maintain for most of the day. The man they call "The Kaiser", however, is a master of social ease and banters good-humouredly with everyone around him, reminiscing about his competitive glory days, discussing his more recent passions for golf and cycling, and voicing concern for the sanitised dullness of today's "too business-like" downhill racing scene.

"What the hell is that?!" is his opening gambit to me as he notices that, among the neat pairs of ski tips poised to shadow him down K70, the first run of the day, I am packing a snowboard, the only tray in the village, and the group's laughter bounces around the soft, forested contours of the Nock Mountains.

With snowboards inherently around 20% slower than skis, I know I'll have my work cut out just to keep Klammer in my sights, and for the first couple of runs, I only come close to his virtually turn-free tracks at the regular stops he makes to allow us all to regroup. So it's ridiculously gratifying when my attempts to channel some of the reckless speed of his Innsbruck triumph (which I've been looping on YouTube) start to pay off, even allowing me, at one glorious moment, to burn off his annoyingly accomplished tangerine shadow. As he stops to wait for stragglers, and I sit down to take a breather, he peers uphill over my head. "Where is our snowboarder? Oh, there you are already. You must be going pretty fast."

The small, traditional resort of Bad Kleinkirchheim (dubbed BKK by British visitors) has been good to Klammer. It was here that he would ski to school from his parents' cattle farm, that he honed his mountain moves, and that he won his first major downhill in 1971's inaugural European Cup. It was also here that, in 2004, a new World Cup course – the pacy highlight of our ski day – was named in his honour.

Other than this swooping, 3km (1.8m) black run, BKK's 103km (64m) network of mainly red runs is a gentle affair, better suiting beginners, leisurely intermediates and families than mileage-hungry thrillseekers. The resort first found fame for its radon-rich local spring waters, whose curative powers were noted in the 11th century. Home to two huge public thermal baths, plus 50-odd hotel spas, BKK has an unrivalled bathing culture for a ski town.

Franz Klammer in action during the 1976 Olympic Games in Innsbruck. Photograph: Alamy

And Klammer's dedication to promoting its charms goes beyond the call of duty. For the duration of our session, he takes care to chat with his guests, offering one-on-one technique tips when he's asked for them, but focusing most of all on making sure everyone feels included and setting a pace that keeps us skiing together in a relaxed but cohesive group.

As we cruise down the last slope of the day, he leads us to a small course where traffic cones, snow-bikes, snow-adapted skateboards and a table laden with schnapps and shot glasses have been set up for a daft It's A Knockout-style competition. Suddenly, I find that I'm head to head with the Kaiser, joining him first at the schnapps table for some "compulsory doping", before we belly-flop onto skateboards to haul ourselves around a comedy slalom course. As it turns out, it's a discipline for which I have some talent, and on the day's final downhill (I swear the course sloped by at least two degrees), Kaisership is mine.

•Sadly, It's a Knockout-style larks are no longer on the menu, but Franz Klammer returns to Bad Kleinkirchheim to ski with up to 50 guests this season at a new event, This Morning the Slope is Mine (badkleinkirchheim.at). The dates are 5 and 21 January and 4 and 25 February, tickets cost €69 (suitable for good skiers only) and include a two-hour ski pass, small warm-up breakfast and brunch. Flights were provided by Ryanair (ryanair.com), which flies from Stansted to Salzburg from around £60 return, excluding charges and fees (Salzburg is a two-hour drive from Bad Kleinkirchheim). Accommodation was provided by the Hotel Thermenwelt Pulverer (+43 4240 744, pulverer.at), where half-board accommodation in winter costs from €115 per person a night, including use of the hotel's spa area

As snow conditions have improved in Scotland in recent years, so have the facilities in its ski centres. We round up what they offer, from the best pistes to where to stay and the best stop for a nice post-piste cake